Question

∫xdx/√(1-4x²), please, quickly. Help!

Answer 1

∫ x/√(1 - 4·x^2) dx

Subst. z = 1 - 4·x^2

1 dz = -8·x dx

dx = -1/(8·x) dz

∫ x/√(z)·(-1)/(8·x) dz

∫ -0.125/√(z) dz

∫ -0.125·z^(-0.5) dz

-0.25·z^(0.5) + C

-0.25·√(z) + C

Resubst.

-0.25·√(1 - 4·x^2) + C